Global stability for an SEI model of infectious diseases with immigration and age structure in susceptibility

Abstract

In this paper, we propose an SEI age-structured model for infectious diseases where the susceptibility depends on the age and with immigration of new individuals into the susceptible, exposed and infectious classes. The existence of a global attractor and the asymptotic smoothness of the solution semi-flow generated by the model are addressed. Using a Lyapunov functional, we show that the unique endemic equilibrium is globally asymptotically stable.